Problem: Simplify the following expression: $\sqrt{50} + \sqrt{2}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{50} + \sqrt{2}$ $= \sqrt{25 \cdot 2} + \sqrt{2}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{2} + \sqrt{2}$ $= 5\sqrt{2} + \sqrt{2}$ Finally, simplify by combining the terms. $= ( 5 + 1 )\sqrt{2} = 6\sqrt{2}$